MATH 242: Analysis 1 (McGill Final)

Currently Playing: Proof: Reverse Triangle Inequality Theorem | Real Analysis

Support the production of this course by joining Wrath of Math to access all my Real Analysis videos plus lecture notes at the premium tier! https://www.youtube.com/channel/UCyEKvaxi8mt9FMc62MHcliw/join 🛍 Check out the coolest math clothes in the world: https://mathshion.com/ Real Analysis course: https://www.youtube.com/playlist?list=PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli Real Analysis exercises: https://www.youtube.com/playlist?list=PLztBpqftvzxXAN05Gm3iNmpz9SkVfLNqC Get the textbook! https://amzn.to/4lNpyNN Business Inquiries: wrathofmathlessons@gmail.com The reverse triangle inequality tells us how the absolute value of the difference of two real numbers relates to the absolute value of the difference of their absolute values. In particular, |x-y| is greater than or equal to | |x| - |y| |. We'll prove this result in today's lesson. We'll need the normal triangle inequality theorem and another useful result about absolute value inequalities to prove today's result. Proof of the triangle inequality theorem: https://www.youtube.com/watch?v=051WWg9twO0 Proof of the absolute value inequality result we use: https://www.youtube.com/watch?v=X7GhczgUy7c Follow Wrath of Math on... ● Instagram: https://www.instagram.com/wrathofmathedu ● Facebook: https://www.facebook.com/WrathofMath ● Twitter: https://twitter.com/wrathofmathedu